English

Sharp resolvent and time decay estimates for dispersive equations on asymptotically Euclidean backgrounds

Analysis of PDEs 2018-10-04 v1

Abstract

The purpose of this article is twofold. First we give a very robust method for proving sharp time decay estimates for the most classical three models of dispersive Partial Differential Equations, the wave, Klein-Gordon and Schr{\"o}dinger equations, on curved geometries, showing under very general assumptions the exact same decay as for the Euclidean case. Then we also extend these decay properties to the case of boundary value problems.

Keywords

Cite

@article{arxiv.1810.01711,
  title  = {Sharp resolvent and time decay estimates for dispersive equations on asymptotically Euclidean backgrounds},
  author = {Jean-Marc Bouclet and Nicolas Burq},
  journal= {arXiv preprint arXiv:1810.01711},
  year   = {2018}
}